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An improved method for constructing formally self-dual codes with small hulls

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Abstract

The hull of a linear code over finite fields is the intersection of the code and its dual code, which has been widely studied due to its wide applications. In this paper, we develop a general method for constructing linear codes with small hulls using the eigenvalues of the generator matrices. Using this method, we construct many optimal Euclidean and Hermitian LCD codes, which improve the previously known lower bound on the largest minimum distance. We also obtain many (near) MDS LCD codes and (near) MDS codes with one-dimensional hull. Furthermore, we give three tables about formally self-dual LCD codes.

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Acknowledgements

The authors would also like to thank the editor and the anonymous referees for helpful comments which have highly improved the quality of the paper.

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Authors and Affiliations

  1. Key Laboratory of Intelligent Computing and Signal Processing, School of Mathematical Sciences, Ministry of Education, Anhui University, Hefei, 230601, China

    Shitao Li & Minjia Shi

  2. State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, 100093, China

    Minjia Shi

  3. Department of Base Courses, Anhui SanLian University, Hefei, 230601, China

    Juan Wang

  4. School of Mathematicai Sciences, Anhui University, Hefei, 230601, China

    Juan Wang

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  1. Shitao Li
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  2. Minjia Shi
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  3. Juan Wang
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Correspondence to Minjia Shi.

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Communicated by J.-L. Kim.

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This research is supported by the National Natural Science Foundation of China (12071001) and 2021 University Graduate Research Project (Y020410077).

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Li, S., Shi, M. & Wang, J. An improved method for constructing formally self-dual codes with small hulls. Des. Codes Cryptogr. 91, 2563–2583 (2023). https://doi.org/10.1007/s10623-023-01210-y

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  • DOI: https://doi.org/10.1007/s10623-023-01210-y

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